Application of Heat and Mass Transfer to Convective Flow of Casson Fluids in a Microchannel with Caputo–Fabrizio Derivative Approach
Bibliographic record
Abstract
Abstract It has been demonstrated that fractional derivatives exhibit a range of solutions that are helpful in the engineering, medical, and manufacturing sciences. Particularly in analytical research, investigations on using fractional derivatives in fluid flow are still in their infancy. Therefore, it is still being determined whether fractional derivatives may be represented geometrically in the mechanics of the flow of fluids. However, theoretical research will be helpful in supporting upcoming experimental research. Therefore, the aim of this study is to showcase an application of Caputo–Fabrizio toward the Casson fluid flowing in an unsteady boundary layer. Mass diffusion and heat radiation are taken into account while analyzing the PDEs that governed the problem. Dimensionless governing equations are formed from the fractional PDEs by utilizing the necessary dimensionless variables. Once the equations have been transformed into linear ODEs, the solution may then be found by applying the Laplace transform technique. Inverting Laplace transforms by Stehfest’s and Tzou’s Algorithm is then used to retrieve the original variables and the solutions as concentration, temperature, and velocity fields. Graphical illustrations sketched using the Mathcad program are used to show how physical parameters affect temperature, velocity, and concentration profiles. Findings show that the velocity, temperature, and concentration profiles have been improved by thermal radiation, mass diffusion, and fractional parameters. The fractional derivative is a more general derivative due to its nonlocal and flexible nature the flow model that is formulated by applying the fractional derivative is suitable to address the memory effect. The present fractionalized results of velocity, concentration, and temperature are more general and applicable to the wide range of orders of fractional derivatives.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".